The Cross Keys stands on Lawrence Street off the King's Road, built in 1708 and, by Wikipedia's account, the oldest pub in Chelsea. It reopened in 2015 after several years closed.
Its history is the hook. The artists Turner, Whistler, and Sargent, the writers Agatha Christie and Dylan Thomas, and the Rolling Stones all passed through. Come for a pint in a 300-year-old room, a seasonal dinner, and a Sunday roast. Skip it if you want cheap drinks, because Chelsea prices apply.